Theorems · Definition · group theory

groupHomology.H1Iso

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) → groupHomology.H1 A ≅ (groupHomology.shortComplexH1 A).moduleCatLeftHomologyData.H

The 1st group homology of A, defined as the 1st homology of the complex of inhomogeneous chains, is isomorphic to cycles₁ A ⧸ boundaries₁ A, which is a simpler type.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree

Cited by

7 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroup